Flag kernels of arbitrary order

TL;DR

This paper extends the concept of flag kernels on homogeneous groups to distributions of any order, demonstrating that convolution operations can be generalized to these new flag kernels under certain conditions.

Contribution

It introduces a generalized framework for flag kernels of arbitrary order and establishes the extension of convolution operations to these kernels.

Findings

Extension of flag kernels to arbitrary order distributions

Convolution operation extended to generalized flag kernels

Conditions under which convolution is well-defined for these kernels

Abstract

The notion of a flag kernel on a homogeneous group is exteded to distributions of arbitrary multidimensional order. It is shown that under natural restrictions on order the operation of convolution admits an extension to thus generalised flag kernels.